An armchair moderator is someone in a forum or chatroom on the Internet that isn't a moderator of the website, yet acts like one. Sometimes this is abbrieviated to "armchair mod". Usually armchair moderators long to be a moderator themselves, so they try to enforce the rules by telling people who break the rules to stop, and to enforce the rules that are usually already read when you enter the website.

Person 1: what up people
Person 2: stfu n00b
Armchair moderator: please refrain from using profanity or from calling anyone "n00bs", it's annoying and immature.